Question

1. in basketball, the term \hang time\ is the amount of time that a player is suspended in the air when making a basket. to win a slam - dunk contest, players try to maximize their hang time. a player’s hang time is given by the equation ( t = 0.5sqrt{h} ), where ( t ) is the time (in seconds) and ( h ) is the height (in feet) of the jump. the second - place finisher of a slam - dunk contest had a hang time of 1 second, and the winner had a hang time of 1.2 seconds. how many feet higher did the winner jump than the second - place finisher?

Explanation:

Step1: Find height of second - place finisher

We are given the formula \(t = 0.5\sqrt{h}\), and for the second - place finisher, \(t = 1\) second.
Substitute \(t = 1\) into the formula: \(1=0.5\sqrt{h_2}\) (where \(h_2\) is the height of the second - place finisher).
First, solve for \(\sqrt{h_2}\): \(\sqrt{h_2}=\frac{1}{0.5}=2\).
Then, square both sides to find \(h_2\): \(h_2 = 2^{2}=4\) feet.

Step2: Find height of winner

For the winner, \(t = 1.2\) seconds. Substitute \(t = 1.2\) into the formula \(t = 0.5\sqrt{h}\): \(1.2 = 0.5\sqrt{h_1}\) (where \(h_1\) is the height of the winner).
First, solve for \(\sqrt{h_1}\): \(\sqrt{h_1}=\frac{1.2}{0.5}=2.4\).
Then, square both sides to find \(h_1\): \(h_1=(2.4)^{2}=5.76\) feet.

Step3: Find the difference in heights

Subtract the height of the second - place finisher from the height of the winner: \(\Delta h=h_1 - h_2\).
We know \(h_1 = 5.76\) and \(h_2 = 4\), so \(\Delta h=5.76 - 4 = 1.76\) feet.

Answer:

The winner jumped \(1.76\) feet higher than the second - place finisher.